Waste heat recovery of the hydrogen–water mixture from high‐temperature water electrolysis by cascade heat pump for steam generation

Waste heat recovery is common in high‐temperature water electrolysis production, but the latent heat from the hydrogen–water mixture is not fully utilized, and the electric heater to generate steam consumes much energy. In this research, a cascade heat pump is proposed to recover the latent heat from electrolysis products and generate steam. The heat pump can save as much as 65% electric energy compared with a single electric heater. Although in some cases, the latent heat is not enough to generate sufficient steam, it can still save 46.1% of energy. Also, this research emphasizes the significant influence of hydrogen and water proportion in electrolysis products. Compared with 80% water proportion, 50% water proportion can save 1.67 MW energy just in the water vaporization process for a 10 MW electrolyzer. The payback period is 3.43 years, which makes it worth investing.


| INTRODUCTION
Heavy dependence on fossil fuels can cause negative impacts on the ecosystem and human health because of pollutants and greenhouse gases. [1][2][3] Because of the economic depression caused by Covid-19 in 2020, carbon dioxide emissions decreased dramatically (32 billion tons). However, emissions increased sharply, driven by a rebound in economic growth (33.9 billion tons). 4 Some influential countries and regions, including China and the European Union, have put forward carbon neutrality targets in response to serious environmental problems. Hydrogen, as a kind of clean fuel, is an alternative choice. At standard temperature and pressure, hydrogen is a colorless and nontoxic gas that can be used as an energy carrier and storage medium with a high heat value. 5 Today's hydrogen production is mainly from natural gas, oil, and coal accounting for 49%, 29%, and 18%, respectively. 6 Though hydrogen is clean energy, hydrogen production causes massive carbon dioxide emissions, so the carbon-free way to produce hydrogen is to use electricity generated from renewable energy. This is regarded as the widespread hydrogen production form in the future. 7 Water electrolysis can be divided into hightemperature water electrolysis and low-temperature one. For water electrolysis, this reaction needs at least 224.49 kJ/mol external energy (electricity) to continue for liquid water at 80°C, based on Gibs Free Energy. However, the energy demand is only 174.74 kJ/mol at 600°C ( Figure 1A). That is why the efficiency of solid oxide electrolysis cell (SOEC) is higher than alkaline electrolysis and proton exchange membrane electrolysis, which usually work at 60-80°C. [8][9][10][11][12] However, the water in high-temperature electrolysis is steam rather than liquid. To provide high-temperature steam for electrolysis, a large amount of energy is required to vaporize and heat the water to the required temperature (>600°C). Therefore, energy-saving technologies in SOEC systems attract much attention. Combining with a marine diesel engine, which provides power for the ship and the SOEC system to utilize high-temperature flue gas and products of SOEC for steam heating, is a solution. This significantly improves the efficiency of hydrogen production and diesel engines. 13 The SOEC system integrated diesel engine and organic Rankine cycle system can recover waste heat of flue gas, which increases overall system efficiency. 14 Zhao et al. 15 find that the recovered energy is insufficient to heat feedstock to the required temperature without an external heat source, and the recommended integration location of the heat source is the water evaporator. Hosseini et al. 16 find that the flameless boiler can generate hightemperature steam for hydrogen production, utilizing the extremely hot exhaust flue gas from the gas turbine.
The latent heat of water is significant. The 25°C liquid water needs 64.87 kJ/mol energy to be heated to 600°C steam. However, 48.19 kJ/mol energy is consumed during the vaporization stage, which accounts for 74.29% ( Figure 1B). Furthermore, in high-temperature electrolysis, the steam cannot be fully converted into hydrogen, so cooling, condensation, and separation of the hydrogen-water mixture are necessary. Industrial waste heat, whose temperature ranges from 200°C to above 400°C can be more easily retrieved than the lowtemperature one. 17 In this process, the latent heat from the hydrogen-water mixture is released when the temperature is below 100°C, which is not sufficient to directly vaporize water. If this released heat can be effectively captured and recycled, and the temperature can be raised, it can be utilized to generate steam, thereby significantly reducing energy consumption. However, the majority of the current research on waste heat recovery in SOEC systems tends to focus on the heat with temperatures above 200°C, while the abundant latent heat, which can be effectively utilized through a heat pump, is often neglected. In this paper, a low-temperature heat recovery system is constructed to investigate the energy consumption associated with the utilization of latent heat.
Using heat pumps to vaporize water is an efficient way to save energy. High-temperature heat pumps can convert waste heat below 100°C, which accounts for up to 2.8% of industrial energy consumption, into highergrade heat above 100°C. 18 Compared with heating steam with an electric heater, a heat pump can utilize the latent heat from water condensation and reduce power consumption. This has received little attention in previous studies about heat recovery in SOEC. Hightemperature heat pumps include single-stage heat pumps and double-stage heat pumps which are cascade heat pumps. Researchers pay much attention to cascade heat pumps because of their lower compression ratio and energy consumption than a single-stage heat pump.
In certain working conditions with appropriate refrigerants, the outlet temperature in the condenser of the hightemperature stage can reach 130-142°C. [19][20][21] The commercial heat pumps in the market can provide an outlet temperature of 130-160°C. 22 These demonstrate the feasibility of steam production through a cascade heat pump.
In conclusion, existing research on waste heat recovery in SOEC systems has predominately focused on heat with high temperatures. Some of them supply waste heat to SOECs to lower electricity demand, [13][14][15][16] while some only focus on producing steam via heat transfer with high-temperature waste heat. 15 The massive latent heat from water condensation is often overlooked. This paper studies the performance of the waste heat recovery system with a cascade heat pump of two stages in recovering phase-transition thermal energy.
The innovations in this work are as follows: 1. Focus on waste heat utilization to generate steam rather than hot water in green hydrogen production 2. Low-grade thermal energy is improved by the heat pump in this system to avoid heat waste. 3. The influence of water proportion is considered, which usually is ignored. 4. The temperature lift in two stages is considered.

| METHODOLOGY
The research is simulated by Aspen Hysys, which is established based on the models of hydrogen production by SOECs, heat transfer, and other devices. The hightemperature hydrogen-water mixture is around 600-800°C. The model will calculate the energy consumption, the mass flow rate of steam generated by the heat pump, and the coefficient of performance (COP). The influencing factors include the water proportion in the hydrogen-water mixture, nine schemes of five refrigerants, and phase-transition temperature.

| Description of the model
The waste heat recovery system used in the current study is shown in Figure 2. A cascade high-temperature heat pump is used to generate steam. It contains a hightemperature stage (HTS) and a low-temperature stage (LTS). The system involves several devices, including evaporators, condensers, compressors, throttles, and a separator.
The hydrogen-water mixture (3) and the oxygen (1) flow into a heat exchanger and be cooled to 50°C; both of them are initially 150°C; then the hydrogen-water mixture (4) flows into a separator, and the liquid water (6) will be separated and mixed with fresh water (7) of 25°C; subsequently the water (8) and be heated to steam (9) of 110°C.
In LTS, the refrigerant (13) obtains the heat from oxygen (1) hydrogen-water mixture (3), the temperature will increase to 40-47°C and becomes saturated (10), after being compressed, the temperature reaches 85-107°C (11), and the thermal energy is subsequently transferred to refrigerant (14) in HTS. The refrigerant (12) flows through the throttle, and the temperature decreases to 40°C (13) and is heated again. In HTS, the refrigerant of 60-90°C (14) will be vaporized into gas (15) by the hot stream (11) and compressed to 120°C (16), which is used to heat liquid water into steam. The refrigerant (17) flows through the throttle, which F I G U R E 2 Systemic process. HTS, hightemperature stage; LTS, low-temperature stage.
becomes cold (14), and is heated again. The temperature in the heat pump cycle is determined by different schemes of refrigerants and phase-transition temperature. The inlet temperature of the hot side in the heat exchanger is at least 10°C higher than the outlet temperature of the cold side. 23

| The investigated refrigerant
The properties of refrigerants have a significant impact on the heat pump's performance. There are several points to consider in selecting suitable refrigerants. Safety is one of the crucial points. According to the Chinese national standard (GB/T7778-2017), refrigerants are classified into eight categories (A1, A2L, A2, A3, B1, B2L, B2, and B3) according to their toxicity and combustibility. 24 Refrigerants in category A are less toxic than those in category B, and a smaller number after the letter means that the refrigerants of that category are less combustible. Also, it is important to choose climate-friendly refrigerants for this system on the request of environmental protection. The global warming potential (GWP) and ozonedepleting potential (ODP) are two important indexes to evaluate the environmental protection of refrigerants. Finally, thermodynamic properties are crucial points to select the refrigerants, which ensure the heat pump's good operation. High thermal conductivity coefficient, large latent heat, small density, and small viscosity are the features of refrigerants that have good thermodynamic properties. The COP and compression ratio are indexed to evaluate the performance of the system which is closely related to refrigerant properties. To generate 110°C steam, refrigerants used in HTS have a critical temperature higher than 120°C. R245fa, R600, R123, R245ca, and R1234ze(E) are chosen for this system, 23 and their properties are shown in Supporting Information: Table S1. The properties of five refrigerants and the heat pump cycle of R245fa are shown in Figure 3.

| Thermodynamic modeling
The inlet temperature of the hot side of the heat exchanger is always higher than that of the cold side. In this study, the former is assumed to be at least 10°C 23 higher than the latter, which ensures the heat flow is not too small. The pinch point of temperature difference in the heat exchanger is another important parameter that is considered to be at least 5°C. 14 The liquid fraction of the refrigerant in the heating cycle also highly affects the performance of the compressor. With high wetness, the compressor is easy to be destroyed and has a much lower efficiency than that with a zero liquid fraction. Therefore, the refrigerant at the inlet of the compressor is considered to be saturated fluid. Furthermore, the performance of the system changes with the isentropic efficiency of the compressor. To better compare the performance variation, the isentropic efficiency is assumed to be constantly 75%. 25 To analyze the investigated system, energy principles were used to examine the heating cycle. The main assumptions in this section were as follows.
1. Flow rate is assumed to be stable. 3. The heat loss of the heat exchangers is considered to be 5%. 13 4. The pressure drop in the heat exchangers is not considered.

| Energy analysis
This model is based on the operation of a SOEC system whose power is 10 MW. The rate of hydrogen flow can be calculated by Equation (1). The molar flow of oxygen is half of the hydrogen.
where m H 2 is the mass flow of hydrogen, 0.083 kg/s; W SOEC is the energy consumption power of SOEC, 10 MW; LHV H 2 is the low heat value of hydrogen, 120 MJ/kg; m O 2 is the mass flow of oxygen, 0.659 kg/s. There are two evaporators in the system with different temperature conditions. The refrigerant exchanges heat with hydrogen-water mixture and oxygen in the evaporator used in LTS. The refrigerant of LTS transfers heat to the refrigerant of HTS in the other evaporator. The thermal energy in the evaporators can be calculated by the equations below.
where h is the enthalpy, MJ/kg; η is the efficiency of the heat exchanger, 95%. m LTS and m HTS are the mass flow rate of refrigerants in LTS and HTS, respectively, kg/s. The thermal energy transferred to water (8) in the condenser of HTS can be calculated by Equation (5).
where W output is the energy output of the heat pump system, MW. The energy consumption of two compressors can be calculated by the equations below.
where η st is the isentropic efficiency of the compressor, 75%.
The electric heater to generate steam from liquid water is the main method in typical SOEC systems. The electricity consumption in different systems can be calculated based on Equations (8)- (11).
where m actual is the mass flow of water used for electrolysis in SOEC, kg/s; W typical is the power consumption of the typical system with a single electric heater to produce steam, MW; Δh is the enthalpy difference of water in two states, MJ/kg; 95% is the heating efficiency of the electric heater; W system is the power consumption of system with the heat pump, MW; W accessary is the energy consumption of the additional electric heater used to meet the steam demand, MW; energy saving proportion (ESP), is the value with heat pump, compared with a single electric heater.

| Economic analysis
In a typical SOEC system, electric heaters are applied to heat the liquid water to steam with a temperature of 600°C, resulting in massive power consumption. To optimize energy utilization, a cascade heat pump is employed to generate 110°C steam, which is then further heated to 600°C via electric heaters. The costs of electric heaters are not taken into consideration, as they are required in both conventional SOEC system and the SOEC system designed in this study. The economic analysis should primarily focus on assessing whether the benefits of electricity savings over a specified time horizon can outweigh the capital investment and operating and maintenance costs of the heat pump. The electricity price is assumed to be 80.9 $/MWh (0.08 $/ kWh) according to the industrial power price in China in 2022.
The costs and the net present value of this project can be calculated by Equations (14)- (20). 26 where C compressor , C heatexchanger , and C throttle are the capital investments of compressor, heat exchanger, and throttle, respectively, $; m refrigerant is the mass flow rate of refrigerants in HTS or LTS, kg/s; γ is the pressure compression ratio; CEPCI is the Chemical Engineering Plant Cost Index; A heatexchanger is the area of heat transfer, m 2 .
 (20) where f INST is the installation factor accounting for the costs of pipes, connections, and other costs in the installation, 0.7; f IC is the indirect cost factor incorporating construction costs, management costs, and service costs, 0.45; f OCC is the contingency cost factor as the costs required to handle unexpected situations; 0.45. Z is the total cost rate is the sum of the capital investment of the components Z C , and operating and maintenance costs Z OM , $/y; CRF is the capital recovery factor; φ r is the maintenance ratio, 1.6; AOH is the annual operating hour of system, 3000 h/year. IR is the interest rate, 10%; y is the expected life cycle of components, 20 years; NPV is the net present value, $; ANS is the annual net saving, $; IF is the inflation factor, 5%.

| Validation
The modeling values are compared with the experiment to show the accuracy. The experimental study is to test the performance of an R134a-R410A cascade refrigeration system with varying intermediate temperatures. 29 Operation data of the experimental system and modeling values calculated by Aspen Hysys are shown in Figure 4. The maximum related error is only 3.7%, so the simulation model is accurate for conducting research.

| Effect of water proportion on recovered energy
The water proportion in the hydrogen-water mixture influences the recovered energy significantly. Different water proportions from 80% to 50% under 1 bar were studied. There are a total of nine schemes of refrigerants in this research. In Schemes 1-3, the refrigerants used in  | 3075 HTS and LTS are the same, which are R245fa, R600, and R123, respectively. In Schemes 4-9, the refrigerants used in HTS and LTS are different. For Schemes 4-6, R245ca is used in LTS, but the refrigerant in HTS is R245fa, R600, and R123, respectively. For Schemes 7-9, R1234ze(E) is used in LTS, but the refrigerant in HTS is still R245fa, R600, and R123, respectively, the same as in Schemes 4-6.
The system's total energy efficiency and isentropic efficiency of compressors will change with the property of refrigerants, phase-transition temperature, and the temperature at the inlet or outlet of the compressor. As mentioned above, the isentropic efficiency can be set as 75% by using a certain superheat degree of inlet temperature and outlet temperature of the compressor. Also, the temperature setting should meet the requirement of the heat exchanger. In LTS, the condensation phase-transition temperature of the refrigerant is 90°C, and the evaporation phase transition temperature is 50°C. In HTS, the condensation phase-transition temperature is 120°C, and the evaporation phase-transition temperature is 80°C.
The simulated results are shown in Figures 5 and 6. When the water proportion decreases from 80% to 50%, the mass flow rate of the hydrogen-water mixture changes from 3.05 to 0.825 kg/s, which decreases by 72.9%. The water supply demand of SOEC decreases from 3.71 to 1.48 kg/s. However, lower water proportion means less available output energy and less steam mass flow rate. The maximum output energy of the heat pump is 11.51 MW in Scheme 8, where the water proportion is 80%. When the water proportion is 50%, the value is only 3.06 MW, which decreases by 73%. The generated water steam reduces from 4.56 to 1.21 kg/s. The second largest one is Scheme 7; the output energy decreases from 11.43 to 3.04 MW with a decrease in water proportion, and the steam mass flow rate decreases from 4.53 to 1.2 kg/s. This is because the decrease of water proportion in the mixture causes a significant decline in steam generation, and the main energy source of the heat pump is the latent heat released during the water liquefaction.
Of the designed nine schemes, Scheme 3 has the highest COP under the same water proportion. For example, when the water proportion is 80%, the COP of Scheme 3 is 2.70 with the ESP of 58.5%. Under the working conditions, the steam generated by the heat pump is more than the demand of SOEC. The energy consumption of two compressors is 3.76 MW. However, the value will be 9.05 MW if the electric heater, which is the main method to generate steam in other SOECs, is applied, so the energy consumption drops by 5.29 MW.
The second highest COP shows in Scheme 6 as 2.66, with the ESP of 57.6%. Compressors consume 3.84 MW of electricity, saving 5.21 MW of energy. The energy-saving ability (5.21 MW) compared with Scheme 3 (5.29 MW) is still well. With the least COP of 2.2, Scheme 8 can also save 3.82 MW of energy.
When the water proportion is not large enough, the available thermal energy of the heat pump is less. Sometimes, the steam generated is less than the SOEC's demand. Therefore, an additional electric heater is necessary, whose energy consumption can be calculated by Equation (13). If the water proportion is 80%, all schemes meet the requirement. However, if the water proportion is 70%, Schemes 3, 4, and 6 cannot meet the steam demand, and the ratio of generated steam to demand is 96.7%, 99.9%, and 97.4%, respectively; the energy consumption of electric heater is 0.19, 0.07, and 0.15 MW, respectively.
The generated steam becomes much less than the required steam with decreasing water proportion. When the water proportion is only 50%, all the schemes need an additional electric heater. The ESP of Scheme 3 and 6 will decrease to 46.1% and 46%, respectively; the electric heater consumes 0.95 and 0.93 MW, respectively. Compared with generating steam only by the electric heater, the energy consumption drops by 1.67 and 1.66 MW, respectively.
The change in water proportion will not influence the COP. Because the energy consumption of the compressor and the output energy of the system are related to the isentropic efficiency of the compressor and the heat pump cycle's working condition. The latter two remain unchanged, so the COP stays the same, but the absolute energy value will change proportionally with input energy.
F I G U R E 5 The generated steam and energy consumption of Schemes 1-3 (two stages with the same refrigerants).

| Effect of phase-transition temperature on recovered energy
The different phase-transition temperature of refrigerant leads to changes in the heat pump cycle, which significantly impacts the system's overall energy efficiency. In this research, the influence of phase-transition temperature on output energy, ESP, and COP is studied under 1 bar pressure with an 80% water proportion. If the phase-transition temperature changes, the output energy from the heat pump is sufficient to generate steam, and the electric heater is not necessary. A total of nine schemes are the same as mentioned above. The different phase-transition temperatures are shown in Table 1.
For each heat pump stage, the higher temperature lift means lower system energy efficiency and more energy consumption of the compressor, but the other heat pump stage has reversed change. Figure 7 shows that, in Schemes 1, 2, and 3, the highest COP shows when difference between LTS and HTS's temperature lift is the smallest, which is combination 1. Higher temperature lift results in higher energy consumption of the compressor and the heating capacity. The consumption is significantly higher than the heating capacity which leads to the drop in the COP. When the same refrigerant is used, the increase in temperature lift has a more obviously negative impact on energy efficiency than the positive influence on the drop of temperature lift in the other stage of the cascade heat pump. Therefore, the system's energy efficiency decreases with the increase in the difference between the two stages' temperature lifts. Scheme 3 has a maximum COP of 2.71 and it decreases to a minimum of 2.64 with a growing temperature difference.
For different refrigerant utilization in LTS and HTS, Combination 1 does not mean the highest COP because the refrigerant's property influences the efficiency significantly.
Though less COP is shown in the smaller difference in temperature lift in two stages using the same refrigerants, it is uncertain for different refrigerants. Figure 8A shows that when the refrigerant is R245ca in LTS (Scheme 4, 5, and 6), Scheme 6 has a maximum COP of 2.68 in Combination 3, compared with a minimum COP of 2.58 in Combination 4. Figure 8B shows that when the refrigerant is R1234ze(E) in LTS (Scheme 7, 8, and 9), Scheme 9 has a maximum COP of 2.56 in Combination 5, compared with a minimum COP of 1.92 in Combination 4. This is because the stage with a higher-performance refrigerant reduces energy consumption more than other refrigerants. The former has a less F I G U R E 6 The generated steam and energy consumption (two stages with different refrigerants) (A) Schemes 4-6. (B) Schemes 7-9. HTS, high-temperature stage; LTS, low-temperature stage.
T A B L E 1 Working temperature of heat pump. | 3077 negative effect on COP than the latter when temperature lift increases. Furthermore, the stage of the lowerperformance refrigerant with decreasing temperature lift may have a more obviously positive impact on energy efficiency than the negative influence from the other stage. The electric heater is not needed when the water proportion is 80% because the generated water steam is sufficient. Therefore, the minimum steam production rate corresponds to the minimum energy consumption of the compressor, because of the unchanged input energy and isentropic efficiency. Scheme 3's refrigerants working under the temperature of Combination 1 have the lowest energy consumption of 3.75 MW with the ESP of 65%. The second least choice is that Scheme 6's refrigerants work under the temperature of Combination 1, with energy consumption of 3.81 MW and ESP of 64.6%. The highest COP and lowest energy consumption may not be shown together because of the different heat pump cycles. Scheme 3 with the shared temperature lift, Combination 1, can be viewed as the most energy-saving choice. If the water proportion changes, the generated steam is less than SOEC's demand, and the flow rate of steam can be improved by changing phase-transition temperature, which saves more energy than an electric heater.

| Economic impact of cascade heat pump system
Schemes of refrigerants used in heat pumps and water proportions have significant impacts on the capital investments of the heat pump. In economic analysis, Scheme 3 is chosen due to its highest COP, and the working condition with a water proportion of 80% is selected as it is the most expensive cost in the same Scheme. The calculation results of costs are shown in Table 2. Figure 9 shows that the investment can earn money in the fourth year, and the payback period is 3.43 years.
The profit of the system comes from cost savings in electricity expenses so the power price has a significant impact on it. In this study, a mean power price is selected, although the actual power price fluctuates monthly. The substantial cost savings result in a short payback time which proves that this project is worth investing via the estimation.
F I G U R E 7 The generated steam and COP of Scheme 1-3 (two stages with the same refrigerants). COP, coefficient of performance; HTS, high-temperature stage; LTS, low-temperature stage.
F I G U R E 8 The generated steam and COP (two stages with different refrigerants) (A) Schemes 4-6. (B) Schemes 7-9. COP, coefficient of performance; HTS, high-temperature stage; LTS, low-temperature stage.
T A B L E 2 The calculation results of costs.